Details

Time bar (total: 4.0m)

sample159.0ms

Algorithm
intervals
Results
43.0ms38×body2560valid
32.0ms182×body80valid
30.0ms34×body1280valid
16.0ms98×body80nan
8.0ms11×body640valid
6.0ms12×body320valid
4.0ms3×body5120valid
1.0ms4×body160valid

simplify253.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
253.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize47.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.2b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
40.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
21.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
119.0ms
(sqrt (fma (* a c) -4 (* b b)))
112.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
95.0ms
(fma (* a c) -4 (* b b))

simplify30.6s

Counts
334 → 252
Calls
334 calls:
Slowest
519.0ms
(fma (- (sqrt (fma (* a c) -4 (* b b)))) 1 (* (sqrt (fma (* a c) -4 (* b b))) 1))
425.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
249.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
249.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (sqrt 2)) (* (cbrt a) (cbrt a)))
246.0ms
(/ (/ (* (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (* (* 2 2) 2)) (* (* a a) a))

prune3.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize51.0ms

Local error

Found 3 expressions with local error:

22.3b
(sqrt (fma c (* -4 a) (* b b)))
1.6b
(- (- b) (sqrt (fma c (* -4 a) (* b b))))
0.1b
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) 2) a)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
208×*-un-lft-identity
138×times-frac
113×add-sqr-sqrt
108×add-cube-cbrt
60×prod-diff
36×distribute-lft-out
34×distribute-rgt-neg-in sqrt-prod
26×distribute-lft-out--
22×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
8×add-cbrt-cube add-exp-log
7×neg-mul-1 add-log-exp
5×div-inv
4×pow1
3×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u
2×diff-log div-sub difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log associate-+l- flip-- associate-/l/
Counts
3 → 217
Calls
3 calls:
Slowest
104.0ms
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) 2) a)
16.0ms
(- (- b) (sqrt (fma c (* -4 a) (* b b))))
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series337.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
125.0ms
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) 2) a)
113.0ms
(- (- b) (sqrt (fma c (* -4 a) (* b b))))
99.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify34.1s

Counts
310 → 226
Calls
310 calls:
Slowest
438.0ms
(/ (/ (* (cbrt (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0)) (cbrt (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
430.0ms
(/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt a))
307.0ms
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) (cbrt 2)) (sqrt a))
302.0ms
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) (sqrt 2)) a)
292.0ms
(/ (/ (+ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) 0) (sqrt 2)) (cbrt a))

prune2.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.8b

localize35.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.2b
(fma (* a c) -4 (* b b))
0.1b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
792×times-frac
512×add-sqr-sqrt
511×*-un-lft-identity
363×add-cube-cbrt
80×associate-/r*
74×distribute-lft-out-- difference-of-squares
70×sqrt-prod
60×prod-diff
58×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
17×div-inv
15×div-exp
13×add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
2×diff-log
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 469
Calls
4 calls:
Slowest
39.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
10.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(sqrt (fma (* a c) -4 (* b b)))
120.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
117.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
82.0ms
(fma (* a c) -4 (* b b))

simplify2.3m

Counts
724 → 481
Calls
724 calls:
Slowest
861.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2)))))
718.0ms
(/ (cbrt 1) (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2))))
660.0ms
(/ 1 (/ (sqrt a) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
602.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ 1 (sqrt 2))))
532.0ms
(/ 1 (/ (* (cbrt a) (cbrt a)) (/ (+ (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt 2) (cbrt 2)))))

prune6.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize76.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (fma (* a c) -4 (* b b)))
22.3b
(sqrt (fma (* a c) -4 (* b b)))
22.3b
(sqrt (fma (* a c) -4 (* b b)))
1.6b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip--
Counts
4 → 139
Calls
4 calls:
Slowest
10.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(sqrt (fma (* a c) -4 (* b b)))
94.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
93.0ms
(sqrt (fma (* a c) -4 (* b b)))
79.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify13.6s

Counts
162 → 151
Calls
162 calls:
Slowest
277.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
233.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
230.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
220.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
220.0ms
(fma (- (cbrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b)))))))

prune3.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.8b

regimes502.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.3b

bsearch134.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.7s1118×body2560valid
1.0s5818×body80valid
733.0ms869×body1280valid
402.0ms2866×body80nan
313.0ms443×body640valid
181.0ms118×body5120valid
104.0ms245×body320valid
30.0ms106×body160valid